Finite Group Databasebeta

← C127×#9342 #44573015

Subgroups — C127×#9342 #44573015

Order 32512.

478 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3195C211yesmaximal, characteristic
2C127×#2378C211yesmaximal, characteristic
3C127×#1996C211yesmaximal, characteristic
4C127×#1511C211yesmaximal, characteristic
5C127×#1508C211yesmaximal, characteristic
6C127×#1305C211yesmaximal, characteristic
7C127×#1284C211yesmaximal, characteristic
8C2×C22⋊Q8×C127C2211yescharacteristic
9C2×C22⋊Q8×C127C2211yescharacteristic
10#483×C127—21no—
11#483×C127C412yescomplemented
12#470×C127—22no—
13#451×C127—21no—
14#451×C127C412yescomplemented
15#407×C127C2211yescharacteristic
16#407×C127C2211yescharacteristic
17#391×C127—21no—
18#389×C127—21no—
19#388×C127—21no—
20#388×C127—21no—
21#387×C127—21no—
22#387×C127—21no—
23#381×C127C2211yescharacteristic
24#380×C127C2211yescharacteristic
25C4×C22⋊C4×C127C2211yescharacteristic
26#342×C127—21no—
27#342×C127—21no—
28#328×C127—22no—
29#328×C127—21no—
30#328×C127—21no—
31C22×Q8×C127C2×C411yescharacteristic
32C22×Q8×C127D411yescharacteristic
33C23×C4×C127C2311yescharacteristic
34C2×Q16×C127—22no—
35C2×M16×C127—21no—
36C2×M16×C127—21no—
37C22⋊Q8×C127—21no—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—21no—
40C22⋊Q8×C127—21no—
41C22⋊Q8×C127—21no—
42C22⋊Q8×C127—21no—
43C22⋊Q8×C127C2×C412yes—
44C22⋊Q8×C127D412yes—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127C2×C411yescharacteristic
51C2×C4⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C2×C22⋊C4×C127—21no—
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127D411yescharacteristic
57C2×C22⋊C4×C127D411yescharacteristic
58C2×C42×C127—21no—
59C2×C42×C127—21no—
60C2×C42×C127—21no—
61#106×C127—22no—
62#103×C127—22no—
63#103×C127—22no—
64C22⋊C8×C127—21no—
65C22⋊C8×C127—21no—
66C22⋊C8×C127—21no—
67C22⋊C8×C127C2×C412yes—
68#95×C127—21no—
69#95×C127—21no—
70#95×C127—21no—
71#95×C127—21no—
72#95×C127—21no—
73#95×C127—21no—
74#95×C127—21no—
75#95×C127D411yescharacteristic
76#95×C127D411yescharacteristic
77C24×C127C2×D411yescharacteristic
78C2×Q8×C127—21no—
79C2×Q8×C127—21no—
80C2×Q8×C127—21no—
81C2×Q8×C127—81no—
82C2×Q8×C127—81no—
83C2×Q8×C127C22⋊C412yes—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—21no—
92C22×C4×C127—41no—
93C22×C4×C127—81no—
94C22×C4×C127C22×C411yescharacteristic
95C22×C4×C127C2×D411yescharacteristic
96C22×C4×C127C2×D411yescharacteristic
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127#4111yescharacteristic
99C22×C4×C127#4111yescharacteristic
100Q16×C127—82no—
101M16×C127—81no—
102M16×C127—81no—
103C2×C8×C127—22no—
104C2×C8×C127—41no—
105C4⋊C4×C127—22no—
106C4⋊C4×C127—22no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—21no—
109C4⋊C4×C127—21no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—81no—
113C4⋊C4×C127—81no—
114C4⋊C4×C127—81no—
115C4⋊C4×C127C22⋊C412yes—
116C22⋊C4×C127—22no—
117C22⋊C4×C127—22no—
118C22⋊C4×C127—22no—
119C22⋊C4×C127—41no—
120C22⋊C4×C127—41no—
121C22⋊C4×C127—41no—
122C22⋊C4×C127—41no—
123C22⋊C4×C127—41no—
124C22⋊C4×C127—81no—
125C42×C127—81no—
126C42×C127—81no—
127C42×C127—81no—
128C23×C127—21no—
129C23×C127—21no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127C4×D411yescharacteristic
133C23×C127#12011yescharacteristic
134C23×C127#12111yescharacteristic
135Q8×C127—42no—
136Q8×C127—42no—
137Q8×C127—81no—
138Q8×C127—81no—
139C2×C4×C127—22no—
140C2×C4×C127—22no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—42no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—41no—
166C2×C4×C127—81no—
167C2×C4×C127—81no—
168C2×C4×C127—81no—
169C2×C4×C127—81no—
170C2×C4×C127C2×C22⋊C411yescharacteristic
171C2×C4×C127C4×D411yescharacteristic
172C2×C4×C127#12111yescharacteristic
173C2×C4×C127#12311yescharacteristic
174C8×C127—42no—
175C8×C127—81no—
176C22×C127—21no—
177C22×C127—21no—
178C22×C127—21no—
179C22×C127—21no—
180C22×C127—21no—
181C22×C127—21no—
182C22×C127—21no—
183C22×C127—21no—
184C22×C127—81no—
185C22×C127—81no—
186C22×C127#38611yescharacteristic
187C22×C127#45511yescharacteristic
188C22×C127#45611yescharacteristic
189C4×C127—21no—
190C4×C127—21no—
191C4×C127—21no—
192C4×C127—21no—
193C4×C127—42no—
194C4×C127—42no—
195C4×C127—81no—
196C4×C127—81no—
197C4×C127—81no—
198C4×C127—81no—
199C4×C127—82no—
200C4×C127—81no—
201C4×C127—81no—
202#9342C12711yesmaximal, characteristic, direct product factor, Sylow
203C2×C127—21no—
204C2×C127—21no—
205C2×C127—41no—
206C2×C127—41no—
207C2×C127#188211yescharacteristic
208C2×C127#190511yescharacteristic
209C2×C127#191311yescharacteristic
210#3195C2×C12711yescharacteristic
211#2378C2×C12711yescharacteristic
212#1996C2×C12711yescharacteristic
213#1511C2×C12711yescharacteristic
214#1508C2×C12711yescharacteristic
215#1305C2×C12711yescharacteristic
216#1284C2×C12711yescharacteristic
217C127#934211yescharacteristic, direct product factor, Sylow
218C2×C22⋊Q8C22×C12711yescharacteristic
219C2×C22⋊Q8C22×C12711yescharacteristic
220#483—21no—
221#483C4×C12712yescomplemented
222#470—22no—
223#451—21no—
224#451C4×C12712yescomplemented
225#407C22×C12711yescharacteristic
226#407C22×C12711yescharacteristic
227#391—21no—
228#389—21no—
229#388—21no—
230#388—21no—
231#387—21no—
232#387—21no—
233#381C22×C12711yescharacteristic
234#380C22×C12711yescharacteristic
235C4×C22⋊C4C22×C12711yescharacteristic
236#342—21no—
237#342—21no—
238#328—22no—
239#328—21no—
240#328—21no—
241C22×Q8C2×C4×C12711yescharacteristic
242C22×Q8D4×C12711yescharacteristic
243C23×C4C23×C12711yescharacteristic
244C2×Q16—22no—
245C2×M16—21no—
246C2×M16—21no—
247C22⋊Q8—21no—
248C22⋊Q8—21no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8C2×C4×C12712yes—
254C22⋊Q8D4×C12712yes—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4C2×C4×C12711yescharacteristic
261C2×C4⋊C4D4×C12711yescharacteristic
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4D4×C12711yescharacteristic
267C2×C22⋊C4D4×C12711yescharacteristic
268C2×C42—21no—
269C2×C42—21no—
270C2×C42—21no—
271#106—22no—
272#103—22no—
273#103—22no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8C2×C4×C12712yes—
278#95—21no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—21no—
283#95—21no—
284#95—21no—
285#95D4×C12711yescharacteristic
286#95D4×C12711yescharacteristic
287C24C2×D4×C12711yescharacteristic
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—81no—
292C2×Q8—81no—
293C2×Q8C22⋊C4×C12712yes—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—81no—
304C22×C4C22×C4×C12711yescharacteristic
305C22×C4C2×D4×C12711yescharacteristic
306C22×C4C2×D4×C12711yescharacteristic
307C22×C4C2×D4×C12711yescharacteristic
308C22×C4#41×C12711yescharacteristic
309C22×C4#41×C12711yescharacteristic
310Q16—82no—
311M16—81no—
312M16—81no—
313C2×C8—22no—
314C2×C8—41no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—81no—
323C4⋊C4—81no—
324C4⋊C4—81no—
325C4⋊C4C22⋊C4×C12712yes—
326C22⋊C4—22no—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—81no—
335C42—81no—
336C42—81no—
337C42—81no—
338C23—21no—
339C23—21no—
340C23—41no—
341C23—41no—
342C23C4×D4×C12711yescharacteristic
343C23#120×C12711yescharacteristic
344C23#121×C12711yescharacteristic
345Q8—42no—
346Q8—42no—
347Q8—81no—
348Q8—81no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4C2×C22⋊C4×C12711yescharacteristic
381C2×C4C4×D4×C12711yescharacteristic
382C2×C4#121×C12711yescharacteristic
383C2×C4#123×C12711yescharacteristic
384C8—42no—
385C8—81no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—81no—
395C22—81no—
396C22#386×C12711yescharacteristic
397C22#455×C12711yescharacteristic
398C22#456×C12711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—42no—
404C4—42no—
405C4—81no—
406C4—81no—
407C4—81no—
408C4—81no—
409C4—82no—
410C4—81no—
411C4—81no—
412C2—21no—
413C2—21no—
414C2—41no—
415C2—41no—
416C2C127×#188211yescharacteristic
417C2C127×#190511yescharacteristic
418C2C127×#191311yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
11. #483×C127C4semidirect
14. #451×C127C4semidirect
202. #9342C127direct (N × H)
217. C127#9342direct (N × H)
221. #483C4×C127semidirect
224. #451C4×C127semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C127×#31952
C127×#23782
C127×#19962
C127×#15112
C127×#15082
C127×#13052
C127×#12842
#9342127